SOMEONE HELP!!
Find the two products below. Compare and contrast, in complete sentences, the similarities and differences of the two.
(x + 6)(x − 6) and (x − 6)(x − 6)

- anonymous

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- katieb

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- anonymous

Find the products first. You have to distribute them.

- anonymous

i need help on how to compare and contrast, brb gotta eat @ttnvnusa

- anonymous

@ttnvnusa

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## More answers

- DebbieG

Well, if you did the FOIL multiplication of each, what did you get?
There should be an obvious difference between them.

- anonymous

uhh so why would they say there is a difference? so why compare and contrast

- DebbieG

Did you FOIL them? What are the products? Start there.

- DebbieG

Yes,like I said, there is a very obvious difference.

- anonymous

who doesnt understand?

- anonymous

right*

- anonymous

florida virtual school

- anonymous

i dont think its wrong

- DebbieG

There is a difference. If you did the FOIL you should see the difference. If you tell me what you got for the products, I can help you from there.

- anonymous

how old are you... you can't spell lol no offense

- DebbieG

Or, if not, I'll just move on.

- anonymous

i did foil.... x^2 - 12x + 36 @DebbieG

- anonymous

yes ***(BECAUSE)*** i'm the dumb one.. you can't spell to save your life

- DebbieG

ok, that's right for one of them. What about the other one?

- DebbieG

And which one did you get that ^^ result for?

- anonymous

the second one @DebbieG

- DebbieG

OK, good, now what about the first one? What did you get for that one?

- anonymous

the first one is .. x^2+12+36 @DebbieG

- DebbieG

No, try again. It's a "special product". That isn't what you get.

- anonymous

hmmmm cause i have a question bout something i don't know a thing? @vk278 wow

- DebbieG

Look at the two binomials, they have a special form.
(a - b)(a + b)
When you take that product, something "special" happens. Do it carefully, one piece at a time F-O-I-L.

- anonymous

something little people like you wouldn't understand :p @vk278

- anonymous

@DebbieG x^2 - 6x + 6x - 36

- DebbieG

OK, good.... now combine those like terms in the middle...

- DebbieG

@JOshua_Lewis what do you get when you combine the like terms?

- anonymous

what do you mean? like do they cancel each other out?

- DebbieG

Well, you can think of it as "canceling" although I don't really care for that word here. Simply add them together, what do you get??

- anonymous

12x

- anonymous

or.. -12x

- DebbieG

Just like you added on the other product: you had -6x-6x and got -12x

- DebbieG

Hmmm... on this one??
You have:
x^2 - 6x + 6x - 36
What is -6x + 6x?

- anonymous

-12x

- DebbieG

What is -6 + 6?

- anonymous

0

- DebbieG

RIGHT. So what is -6x + 6x???

- anonymous

at first that's why i said "canceled out"

- anonymous

x^2-36?

- DebbieG

Right, and I said " you can think of it as "canceling" although I don't really care for that word here. Simply add them together, what do you get??"
It's more like they offset each other. But if you like to think of it as canceling, that's fine. I didn't mean to mislead you. :)

- DebbieG

Exactly! So you have:
\((x-6)(x+6)=x^2-36\)
And
\((x-6)(x-6)=x^2-12x +36\)
do you see some differences that you can compare and contrast? About what you end up with, in each case?

- anonymous

IDK how to exactly word it

- DebbieG

These are both what are often called "special products"....
\((x-6)(x+6)\) is the "product of a sum and a difference" and that always gives you a "difference of squares"... the middle terms of the FOIL will go away, since they "offset" (or cancel :)
\((x-6)(x-6)=(x-6)^2\) so that is a "perfect square". It always takes a very specific form (depending on whether the binomial you square is a SUM or a DIFFERENCE):
\((x-a)^2=x^2-2ax+a^2\)
\((x+a)^2=x^2+2ax+a^2\)

- DebbieG

Well, put it in your own words. The key is the difference in how the FOIL product ends up working out. The "magic" in the product of a sum and a difference is the way the middle terms go away, and leave you with a DIFFERENCE OF SQUARES.

- DebbieG

\((x-a)(x+a)=x^2-ax+ax-a^2=x^2-a^2\)

- anonymous

well thank you very much! i will for sure come back to you if i have any questions. :)

- DebbieG

Sure thing, happy to help! :)

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